Optimal Coordinated Control of Power Extraction in LES of a Wind Farm with Entrance Effects

Abstract

Abstract:We investigate the use of optimal coordinated control techniques in large eddy simulations of wind farm boundary layer interaction with the aim of increasing the total energy extraction in wind farms. The individual wind turbines are considered as flow actuators, and their energy extraction is dynamically regulated in time, so as to optimally influence the flow field. We extend earlier work on wind farm optimal control in the fully-developed regime (Goit and Meyers 2015, J. Fluid Mech. 768, 5-50) to a 'finite' wind farm case, in which entrance effects play an important role. For the optimal control, a receding horizon framework is employed in which turbine thrust coefficients are optimized in time and per turbine. Optimization is performed with a conjugate gradient method, where gradients of the cost functional are obtained using adjoint large eddy simulations. Overall, the energy extraction is increased 7% by the optimal control. This increase in energy extraction is related to faster wake recovery throughout the farm. For the first row of turbines, the optimal control increases turbulence levels and Reynolds stresses in the wake, leading to better wake mixing and an inflow velocity for the second row that is significantly higher than in the uncontrolled case. For downstream rows, the optimal control mainly enhances the sideways mean transport of momentum. This is different from earlier observations by Goit and Meyers (2015) in the fully-developed regime, where mainly vertical transport was enhanced.

Towards practical dynamic induction control of wind farms: analysis of optimally controlled wind-farm boundary layers and sinusoidal induction control of first-row turbines

“…The filtered Navier-Stokes momentum and continuity state equations in Eqs. (2)-(3) are solved using an in-house LES solver (see, e.g., Calaf et al, 2010;Meyers and Meneveau, 2010;Goit et al, 2016 for a detailed discussion of the solver). The time-filtering state equation in Eq.…”

“…For instance, a Strouhal number St = 0.25 corresponds here to a sine wave period of ≈ 50 s for a turbine with diameter D = 100 m and a freestream velocity U ∞ = 8.5 m s −1 . For instance, considering the NREL 5MW blade profiles, the maximum thrust coefficient of 3.5 can be attained by slightly changing the rotor design, e.g., using a 50 % increase in blade chord length and an operational tip speed ratio 25 % higher than the original design value (see Appendix A in Goit and Meyers, 2015). Furthermore, given such redesign, dynamic reductions from this value could be realized through blade pitch control, for which actuation rates of the order of 10 • s −1 are possible (see, e.g., Jonkman et al, 2009).…”

“…The methodology was applied to the asymptotic case of a fully developed "infinite" aligned wind farm, and power gains of about 16 % were quantified. Later, this approach was also used in induction control studies of wind farms with entrance effects in Goit et al (2016) and more recently in Munters and Meyers (2017), in which similar gains of the order of 15-20 % were achieved. It is important to note that the computational cost of this LES-based dynamic induction control methodology is orders of magnitude too high for direct implementation as a practical control strategy.…”

“…In contrast to the studies cited above that all focus on the static set point optimization of wind farms, Goit and Meyers (2015) introduced a dynamic induction control approach based on large-eddy simulations (LES) and adjoint gradient optimization. In this study, individual turbines were used as dynamic flow actuators that influence the wind-farm boundary layer flow in such a way as to optimize aggregate windfarm power extraction.…”

“…Recently, the methodology of Goit and Meyers (2015) was generalized to include dynamic yaw control in Munters and Meyers (2018). In this study, induction control and yaw control were compared for a relatively small aligned wind farm, and yaw control was found to yield higher power gains for this setup.…”